Journal of Magnetism and Magnetic Materials 378 (2015) 246–252
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Structural and magnetic characterization and cation distribution of nanocrystalline CoxFe3 xO4 ferrites Adel Maher Wahba a,n, Mohamed Bakr Mohamed b,c a
Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Egypt Physics Department, Taibah University, Al-Madinah Al-Munawara, Saudi Arabia c Ain shams University, Faculty of Science, Physics Department, Cairo, Egypt b
art ic l e i nf o
a b s t r a c t
Article history: Received 25 September 2014 Received in revised form 30 October 2014 Accepted 30 October 2014 Available online 5 November 2014
Structural and magnetic properties have been investigated for CoxFe3 xO4 nanoferrites (x ¼0.5–1.2, with a step increment of 0.1) prepared by a citrate-precursor autocombustion method. X-ray diffraction patterns (XRD) and Fourier-transform infrared (FTIR) spectra prove the formation of a cubic spinel phase of CoFe2O4, besides x-dependent FeCo2O4 spinel for samples with x Z 0.7. Size of the formed nano-crystals ranges from 34 to 45 nm, which is further confirmed with a TEM micrograph. Investigating magnetic parameters such as saturation magnetization, coercivity, and remanence field, through vibrating sample magnetometry (VSM) data, revealed a strong dependence of the magnetic properties of each sample on its own cation distribution being suggested according to the experimental results of XRD, VSM, and IR data. & 2014 Elsevier B.V. All rights reserved.
Keywords: Autocombustion method Nanoferrites Rietveld Magnetic properties Cation distribution
1. Introduction Magnetic ferrites in the nanoregime are considered as the field of interest for many researchers due to their enormous applications, including magnetic recording, biomedicine, catalysts, etc. [1]. As a principle, the physical properties of nanoferrites are remarkably different from those of their bulk counterparts. The magnetic properties of any prepared nanoferrite are strongly dependent on the particle size [2], method of preparation [3] and, in addition, on the presence of non-collinear spin structure or local spin canting [4]. The nanoscale spinel ferrite has a face-centered cubic (fcc) structure of the form MFe2O4, where M is a divalent atom. The structure contains two interstitial sites occupied by metal cations, namely tetrahedral (A) site and octahedral (B) site. This produces a different local symmetry. The cationic distribution in octahedral and tetrahedral sites is characterized by the inversion parameter γ defined as the fraction of divalent ions in the octahedral sites. The net magnetization, being proportional to the difference between A and B sublattice magnetization, depends on the cationic distribution. In the same manner, since single-ion anisotropy of a specified ion depends on the interstitial site, magnetic anisotropy also depends on the inversion degree. Moreover, several techniques have been used to study the spin-canting phenomenon such as neutron n
Corresponding author. E-mail address:
[email protected] (A.M. Wahba).
http://dx.doi.org/10.1016/j.jmmm.2014.10.164 0304-8853/& 2014 Elsevier B.V. All rights reserved.
diffraction and 57Fe Mössbauer [5,6]. Results provided evidence that spin canting can be either restricted to a single or extended to both cationic sites. Cobalt ferrite is a hard magnetic material highly suitable for applications including long-term storage of magnetization. It is characterized by its high cubic magnetocrystalline anisotropy [7]. Magnetic properties of cobalt ferrite could be precisely adjusted by controlling the inversion parameter and the relative presence of Fe3 þ and Co2 þ cations in the octahedral site in the ferrite system CoxFe3 xO4 [8–10]. In this work, the CoxFe3 xO4 (0.5 rx r1.2, step 0.1) system has been prepared via citrate-precursor autocombustion method. Structural properties including lattice parameter, crystallite size, XRD density, etc. were analyzed using Rietveld software. The absorption peaks of FTIR data were used to confirm the spinel-phase formation and to trace the variation of the sublattice radii. The dependence of the magnetic properties on the cobalt content and their relation with the presence of canting mechanism in the magnetic moment of Fe3 þ cations in the B site have also been investigated.
2. Experimental Nanocrystalline cobalt ferrites with the formula CoxFe3 xO4 (x¼0.5–1.2, step 0.1) were prepared by citrate precursor method. Analytical grade metal nitrates Co(NO3)2 6H2O and Fe(NO3)3 9H2O, and dehydrated citric acid C6H8O7 were used as starting materials.
A.M. Wahba, M. Bakr Mohamed / Journal of Magnetism and Magnetic Materials 378 (2015) 246–252
Fe2O3 0.5 0.6 0.7 0.8
(620) (622)
(440)
(422) (511)
(400)
(311)
1.0
(220)
0.9 (111)
Intensity (a. u.)
x = 1.2 20
(533)
1.1 (222)
The detailed method of preparation is described in a previous work [11]. The autocombustion reaction, reported to occur at nearly 200 °C for cobalt ferrite, produced burnt fluffy ash-like powder. The coarse powder was collected and slightly grounded in a mortar agitate to achieve a fine powder. To confirm the formation of spinel phase structure, XRD patters of the prepared samples were obtained using a Philips diffractometer (X’pert MPD) with a goniometer using Cu-Kα radiation. The diffracted intensities were collected in the step-scan mode (step size 2θ ¼0.015°, counting time 1.5 s) with the angular range 10–80°. To correct instrumental broadening LaB6 standard was used. The crystal structure and microstructure were refined applying Rietveld profile method, using MAUD program [12]. Lattice parameter (a) and crystallite size (D) were obtained as results of Rietveld analysis. The XRD density of the prepared samples were calculated from the formula ρXRD = 8Mw /NAa3, where the factor 8 indicates the number of formula units in a unit cell, Mw is the molecular weight, NA is Avogadro’s number and a3 is the cell volume. The powder morphology was recorded by transmission electron microscope (TEM, JEOL JEM-100CX) with accelerating voltage up to 100 kV. Infrared spectroscopy (IR) (Bruker Tensor 27 FTIR Spectrometer) was used in the range of 200–1000 cm 1 to confirm the spinel-phase formation and help provide a primary assumption of the cation distribution by tracing the variations of the frequencies of the absorption peaks. For this purpose, quantities of 0.2 mg ferrite per 200 mg KBr were mixed and pressed into pellets. The magnetization, remanence, and the coercive fields data were obtained by tracing M–H hysteresis loops for the powder samples at room temperature using the LDJ vibrating sample magnetometer (VSM) model 9600 with a magnetic field extending up to 20 kOe.
247
30
40
50
60
70
2 θ (degree) Fig. 1. X-ray powder diffraction pattern for CoxFe3 xO4 (0.5 r xr 1.2) as-prepared samples.
3. Results and discussion 3.1. Structural analysis XRD patterns of CoxFe3 xO4 (x ¼0.5–1.2, with a step of 0.1) are shown in Fig. 1. The peaks can be indexed with space group Fd3m to (111), (220), (311), (222), (400), (422), (511) and (440) planes of a cubic unit cell. All XRD patterns were analyzed by using MAUD program that is based on Rietveld method [13]. The Rietveld refinement patterns for Co0.5Fe1.5O4 and CoFe2O4 are shown in Fig. 2. Samples with x¼0.5 and 0.6 showed few traces of a second phase of hematite (Fe2O3) with percentages of 10% and 2%, respectively. Similar observation was recorded by Bhowmik in his work with bulk Co0.3Fe2.7O4 regardless the method of preparation [14]. All the observed peaks in the XRD patterns of the other samples (x Z0.7) are located at the Bragg 2θ positions of the spinel phase, which confirm that those samples are single-phase cubic spinel ferrites. The oxygen positions (x¼ y¼z ¼u) were taken as free parameters and all other atomic fractional positions were considered as being fixed. Other parameters such as lattice constants, isothermal parameters, scale factors and shape parameters were considered as free parameters. The sites occupancies distribution in spinel ferrite was obtained from combination of XRD, magnetization and IR data, as we will be seen later. Table 1 illustrates values of D, a, ρXRD, and oxygen parameter u, for the studied samples. The variation of both the lattice parameter and the XRD density with the cobalt content is shown in Fig. 3. Since the ionic radius of Co2 þ is larger than that of Fe3 þ in either A-or B-site, the lattice parameter a is expected to increase monotonically with increasing cobalt content. However, the lattice parameter showed a drop at x ¼0.7 and a slight decrease for x41. This behavior could be explained in terms of the presence of Co3 þ and Fe2 þ cations in the prepared samples. This will be explained in detail when discussing the
Fig. 2. Rietveld refinement profile for (a) Co0.5Fe2.5O4 and (b) CoFe2O4 samples.
cation distribution and the magnetic properties of the samples. The inverse trend between ρXED and a in Fig. 3 indicates that the inverse proportion of ρXED with a3 dominates its direct proportion with the molar mass M. The sharp drop of the crystallite size at x¼ 0.7 (see Table 1) may be attributed to the absence of the phase
248
A.M. Wahba, M. Bakr Mohamed / Journal of Magnetism and Magnetic Materials 378 (2015) 246–252
Table 1 Lattice parameters and phases percentage of CoxFe3 xO4 (0.5 r xr 1.2) obtained from Rietveld refinement. x
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
a (Å)
ρXRD (g/cm3)
D (nm)
8.3675(7) 8.3706(3) 8.3620(2) 8.3777(1) 8.3813(4) 8.3873(7) 8.3866(3) 8.3850(1)
88 56 52 53 49 55 41 35
5.285 5.286 5.310 5.287 5.287 5.283 5.291 5.301
8.39
u
Phase %
0.3766 0.3761 0.3773 0.3764 0.3771 0.3782 0.3773 0.3783
Spinel
Fe2O3
90 98 100 100 100 100 100 100
10 2 — — — — — —
ν1 (cm 1)
ν2 (cm 1)
570.91 572.84 572.84 576.70 576.70 574.77 568.99 568.99
385.75 383.82 385.75 385.75 383.82 379.97 381.90 385.75
5.31
8.38
5.30
8.37 5.29 8.36 5.28 0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Fig. 3. Lattice parameter (a) and XRD density (ρXRD) as deduced from Rietveld analysis for CoxFe3 xO4 (0.5 r xr 1.2) samples.
impurity of hematite recorded for the sample with x ¼0.5. The oxygen positional parameter or anion parameter (u) depends on the chemical composition, preparation conditions and sintering procedure, and can be obtained from Rietveld refinement of XRD data. When the center of symmetry is considered at (¼¼¼) (origin at B-site), the ideal value of parameter u is 0.25, but when assuming center of symmetry at (3/83/83/8) (origin at A-site), uideal is 0.375. At these ideal values, the arrangement of O2 ions correspond exactly to a cubic closed packing, while in actual spinel lattice, this ideal pattern is slightly deformed. For the present CoxFe3 xO4 system, we can see from Table 1 that u is slightly greater the 0.375 indicating that O2 ions move away from the cations in tetrahedral A-site along the 〈111〉direction due to the expansion of the tetrahedral interstices; correspondingly the octahedral B-sites become smaller. This leads to a decrease in the A–A interaction and an increase in the B–B interaction. Worth to mention is that the change in u parameter is not systematic with increases Co content. Fig. 4 shows the TEM images for Co1.2Fe1.8O4 sample. The particles generally have a spherical shape with a relatively homogeneous size and tend to agglomerate due to their mutual magnetic interactions. The matching between the crystallite size revealed from the TEM image and that obtained from Rietveld method is quite reasonable. The FT-IR spectroscopy is an effective technique in expecting the positions of the ions involved in the crystal lattice through their vibrational modes. The infrared spectra of the ferrite samples CoxFe3 xO4 are shown in Fig. 5. The spectra exhibit the major two peaks corresponding to the spinel structure. The first is the higher frequency one for which ν1 ranges from 569 to 577 cm 1 and is attributed to the Fe3 þ –O stretching vibration at the tetrahedral site. The second is the lower frequency one in the range of 380–386 cm 1 and corresponds to the bending vibrations at the octahedral site. Both ν1 and ν2 are listed in Table 1. The shoulders appearing at ν≅660 cm 1 for samples with x Z0.7 correspond to
Fig. 4. TEM micrograph of the Co1.2Fe1.8O4.
the formation of the spinel FeCo2O4 [6,15–17] and/or Co3O4 phase [14,18,19], which either indicates the presence of Co3 þ cation. The broad peak recorded at ν ¼459 cm 1 for the samples with x ¼0.5 and 0.6 is a typical peak for the α-Fe2O3 phase [14], whose traces appeared in XRD patterns of the same samples. 3.2. Magnetic properties analysis The magnetic hysteresis loops for the samples of the present work are shown in Fig. 6. These curves have been used to obtain the magnetization at an applied field strength of H ¼20.0 kOe, M20, the saturation magnetization, Ms (obtained by interpolating M–H curves as H approaches 1 [20]), remanence magnetization, Mr, the coercive field Hc, and the squareness ratio (SQ ¼ Mr/Ms), the values of all are listed in Table 2. Values of SQ reflect the magnetocrystalline anisotropy and the superexchange interactions of the investigated nanoferrites [21]. All our investigated samples have SQ values so close to the 0.5 value that suggests our samples composed of pseudo-single-domain particles. This, besides the recorded crystallites’ size and coercivity, indicate that the surface
A.M. Wahba, M. Bakr Mohamed / Journal of Magnetism and Magnetic Materials 378 (2015) 246–252
249
75 x = 0.5 x = 0.6 x = 0.7
50
M (emu/g)
0.5
0.6
Transmittance (a. u.)
0.7
25 0 -25 -50
0.8 0.9
-75 -20 -15 -10 -5
0
5
10 15 20
0
5
10 15 20
0
5
10 15 20
1.0
75 x = 0.8 x = 0.9
1.1
M (emu/g)
50 x =1.2
800
700
600
500
400
300
-1
25 0 -25
Wavenumber (cm )
-50
Fig. 5. IR spectra for CoxFe3 xO4 (0.5 r xr 1.2) as-prepared samples. Arrows point to shoulders of FeCo2O4 spinel phase.
75 x = 1.0 x = 1.1 x = 1.2
50
M (emu/g)
canting effects could be somehow ignored when compared to local canting effects resulting from the strong magnetocrystalline property of the Co2 þ cations, as will be discussed below. The variation of Mr and Ms with Co content shows exactly the same trend, as expected from the SQ values. Upon increasing x from 0.5 to 0.6 and despite the reduction of the content of highly coercive hematite, Ms decreases and Hc increases. This could be explained in the light of the significant reduction of the crystallite size (D) from 88 to 56 nm (Table 1) and the increase of the Co2 þ cation content in the B site. With increasing x to 0.7, Ms increases despite the reduction of Fe3 þ content in the B site, probably to the disappearance of the hematite phase or, in other words, the reduction of Fe2 þ content. For samples with x ¼0.8 up to 1.0, Ms increases so slowly despite the continuous reduction of Fe3 þ content in the B site and the nearly constant crystallite size. The only possibility to explain that is the depression of the local canting effect induced on the magnetic moments of the B-site Fe3 þ cations [5]. This possibility is further supported by the recorded decrease of Hc with changing x from 0.7 to 1.0. With further increasing x up to 1.2, the reduction of both Fe3 þ content in the B site and the crystallite size lead to a sharp decrease of Ms with a following increase of Hc [22]. Since the magnetic moment of Co2 þ (3 μB) is less than that of 3þ Fe (5 μB), increasing Co2 þ content is theoretically supposed to reduce Ms monotonically. In addition, Increasing Co content enhances the possibility of producing Co3 þ cations (0 μB) during the autocombustion process (see IR data), and according to electron neutrality, this is associated with a production of Fe2 þ (4 μB). Both Co3 þ and Fe2 þ prefer the occupation of B site, and thus, further reduce the overall magnetization. On the other hand, the first member of our series, i.e., the nonstoichiometric Co0.5Fe2.5O4 compound implies the presence of excess of electrons, and thus, a significant portion of Fe cations will be in the form of Fe2 þ . Increasing x above the 0.5 value reduces that nonstoichiometry, and so the concentration of Fe2 þ decreases probably faster than that of Fe3 þ , and thus contributes positively to magnetization. Those two opposing effects, besides the variant local canting, could explain
-75 -20 -15 -10 -5
25 0 -25 -50
-75 -20 -15 -10 -5
H (kOe) Fig. 6. Room-temperature M–H loops for CoxFe3 xO4 (0.5 r xr 1.2) as-prepared samples.
the absence of a single trend for the variation of both Ms and Mr with increasing x. The same argument could also explain the behavior of Hc with increasing Co content. Coercivity of our samples Table 2 Magnetic properties of CoxFe3 xO4 (0.5 r xr 1.2) samples. x
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Mr (emu/g)
M20 (emu/g)
Ms (emu/g)
Hc (kOe)
nexp
36.60 33.40 34.97 35.42 35.17 34.98 31.70 29.31
67.96 64.08 66.90 67.77 67.81 67.64 62.74 57.13
72.38 68.80 71.83 72.69 72.79 72.86 67.70 61.84
1.226 1.461 1.581 1.516 1.511 1.417 1.419 1.641
3.020 2.875 3.006 3.046 3.054 3.061 2.848 2.605
SQ
rA (Å)
rB (Å)
0.506 0.485 0.487 0.487 0.483 0.480 0.468 0.474
0.50827 0.50737 0.50764 0.50611 0.50611 0.50674 0.50980 0.50989
0.67963 0.68128 0.67790 0.68469 0.68605 0.68793 0.68590 0.68524
(μB)
250
A.M. Wahba, M. Bakr Mohamed / Journal of Magnetism and Magnetic Materials 378 (2015) 246–252
Table 3 Cation distribution of CoxFe3-xO4 (0.5 r xr 1.2) samples. x
Cation distribution
θB (deg)
MB
MA
nB
0.5
+ + + 3+ 3+ ⎤ 2− Fe0.797 Fe20.293 Fe1.410 (Co20.203 )⎡⎣Co20.297 ⎦O4.104 2+ 3+ 2+ 3+ 2+ 3+ ⎤ 2− ⎡ (Co0.193Fe0.807)⎣Co0.399Co0.008Fe0.244Fe1.349 ⎦O4.082 2+ 3+ ⎡Co2 + Co3 + Fe2 + Fe3 + ⎤O2 − Co Fe ( 0.196 0.804)⎣ 0.441 0.063 0.177 1.319⎦ 4.093 + + + 3+ 3+ 3+ ⎤ 2− Fe0.821 Co0.082 Fe20.210 Fe1.169 (Co20.179 )⎡⎣Co20.539 ⎦O4.036 2+ 3+ 2+ 3+ 2+ 3+ ⎤ 2− ⎡ (Co0.179Fe0.821)⎣Co0.627Co0.094Fe0.168Fe1.111⎦O4.013 + + + 3+ 3+ 3+ ⎤ 2− Fe0.814 Co0.162 Fe20.195 Fe0.991 (Co20.186 )⎡⎣Co20.652 ⎦O3.984 2+ 3+ 2+ 3+ 2+ 3+ ⎤ 2− ⎡ (Co0.220Fe0.780)⎣Co0.660Co0.220Fe0.174Fe0.946⎦O3.973 + + + 3+ 3+ 3+ ⎤ 2− Fe0.779 Co0.252 Fe20.123 Fe0.898 (Co20.221 )⎡⎣Co20.727 ⎦O3.965
38.06
7.614
4.594
3.020
37.99
7.489
4.614
2.875
0.6 0.7 0.8 0.9 1.0 1.1 1.2
is closely related to the strong magnetocrystalline anisotropy of the Co2 þ cations in the B site. This is not only related to the concentration of Co2 þ cations but also to its environment of Fe3 þ cations and the ability of the former to induce canting effect on the magnetic moments of Fe3 þ [5]. 3.3. Suggested cation distribution Values of Ms were used to estimate experimental values for the magnetic moment per unit formula nexp (listed in Table 2) with the empirical relation nexp = Mw × Ms/5585 [23]. According to Neel’s two sublattice model of ferrimagnetism, cation distribution for the different samples was suggested in such a way that the theoretical value nB ¼MB–MA matches with nexp . The sublattice magnetization MA and MB are estimated from the Bohr magneton of each element: μB ¼ 5, 4, 3, and 0 for Fe þ 3, Fe þ 2, Co þ 2, and Co þ 3, respectively. In estimating MB, we used the model suggested by Peddiset al. [24], in which Fe3 þ cations in the B site are assumed to possess an effective magnetic moment Meff ¼5 cos θB, where θB is the canting angle induced on Fe3 þ cations in B site. Table 3 illustrates the suggested cation distribution for the studied samples and values of θB, MA, MB, and nB. Values of θB listed in Table 3 match well with the reality that the limit of canting is controlled by recognizing how many B-site Fe3 þ ions interact with how many nearest neighbors of A-site Co2 þ ions [25]. Worth to mention is that the variation of the (estimated) Fe2 þ content in the B site is quite similar to the variation of the (experimental) crystallite size, as illustrated in Fig. 7, the fact that confirms the relationship between cation distribution and grain size [26]. This suggests the presence of non-distinguishable spinel structure more than that of the CoxFe3 xO4 such as FeCo2O4, and/
Fig. 7. Comparison between variation of the estimated Fe2 þ content in the B site and the experimental crystallite size for CoxFe3 xO4 (0.5r x r1.2) samples.
32.16
7.614
4.608
3.006
26.50
7.688
4.642
3.046
22.20
7.696
4.642
3.054
0.00
7.691
4.628
3.063
0.00
7.406
4.560
2.846
0.00
7.163
4.558
2.605
or magnetite (Fe3O4) [27,28]. For all such iso-structural phases exhibiting solid solution behavior, it is so difficult to identify accurately the chemical composition of the formed spinel phase [29]. Besides magnetization data, lattice parameters and IR data were used to further improve the reliability of the suggested cation distribution. We performed a theoretical estimation of the lattice parameter for each composition and compared it with that obtained by Rietveld method. The average ionic radii per molecule of the tetrahedral and octahedral sites, rA and rB, respectively, were calculated based on the cation distribution of Table 3, using the formulae [30]
rA =
∑i αiri
&
rB =
1 2
∑i αiri
where αi is the concentration of the element i of ionic radius ri on the respective side. The used ionic radii were for Co þ 2 (0.745 Å in B-site and 0.58 Å in A-site), Fe þ 3 (0.645 Å in B-site and 0.49 Å in A-site), Co þ 3 (0.61 Å in B-site), and Fe þ 2 (0.78 Å in B-site). Then, we got the theoretical values of the lattice parameter from the relation [30] :
a th =
8 ⎡ ⎣(rA + R O) + 3 3
3 (rB + R O)⎤⎦
where RO is the ionic radius of oxygen. The estimated values of ath match to the fourth decimal with that estimated from XRD data. Values of rA and rB are listed in Table 2. Three experimental results are strongly supporting the estimated values of rA and rB. First, the variation of rB and a with x are quite similar, as illustrated in Fig. 8, where significant changes of cation distribution upon changing x is expected to occur in the B site. Second, the variation of rB and Hc with x (and excluding x ¼0.5 due to the hematite effect) is quite opposite (Fig. 9). Smaller rB value provides strong spin-orbit
Fig. 8. Comparison between the variation of the octahedral sublattice radius rB and the lattice parameter a with the Co2 þ content x for CoxFe3-xO4 (0.5r x r1.2) samples.
A.M. Wahba, M. Bakr Mohamed / Journal of Magnetism and Magnetic Materials 378 (2015) 246–252
0.690 1700
0.685
1600
Table 4 Estimated cation distribution analysis for CoxFe3 xO4 (0.7 r xr 1.2) spinel nanoferrite system. Composition Cation distribution ( 70.001)
1500
0.680
Co0.7Fe2.3O4
1400 Co0.8Fe2.2O4
0.675 0.6
0.7
0.8
0.9
1.0
1.1
1.2 Co0.9Fe2.1O4
Fig. 9. Comparison of the variation of the octahedral sublattice radius rB and the coercivity Hc with the cobalt content for CoxFe3 xO4 (0.6 r xr 1.2) samples.
CoFe2O4 Co1.1Fe1.9O4
coupling, large cubic crystalline anisotropy constant, and thus enhanced coercivity [20]. Third, the variation of the sublattice radii rA and rB with x shows quite opposite trend with the variation of the values of ν1 and ν2 recorded from IR data (Fig. 10), where shorter bond corresponds to higher vibrational frequency. In order to further confirm this suggested cation distribution for the single phase samples (xZ0.7), Bertau method [31] was applied. Bertau method relies on the choice of some of few reflections known to be sensitive to cation distributions, such as I220 /I400, I220/I422 and I422/I440 [32]. The refinements of these chosen reflections were done, by minimizing the R-factor which is equal to [32]:
⎛ I Obs ⎞ ⎛ I Cal ⎞ ⎟⎟ − ⎜⎜ hkl ⎟⎟ R = ⎜⎜ hkl , , ,⎠ , , ,⎠ ⎝ IhObs ⎝ IhCal kl kl
578
0.512
0.506
1.0
I220/I440 Exp. Cal.
1.45
1.16
0.63
0.71
0.92
0.82
1.46
1.23
0.67
0.69
0.97
0.85
1.57
1.14
0.69
0.78
1.09
0.89
1.52
1.21
0.67
0.72
1.01
0.89
1.56
1.15
0.63
0.77
0.99
0.89
1.57
1.36
0.67
0.63
1.04
0.86
All the observed intensities (Iobs) for the corresponding planes have to be corrected first by using Buerger formula:
Ihkl = |F |2hkl PL p, where F is the structure factor, P is the multiplicity factor and Lp is the Lorentz polarization factor for each (hkl) [33]. The displacement parameters corrections were not used due to its negligible small values. The best cations distribution obtained from Bertau method were subjected to further refinements using Rietveld method and are shown in Table 4, the obtained cations distributions are reliable with what being obtained from magnetic measurements.
4. Conclusion
References
570
0.8
I400/I440 Exp. Cal.
0.684
0.508
0.6
I220/I400 Exp. Cal.
0.689
0.510 574
568
Co1.2Fe1.8O4
(Co0.196Fe0.804)A [Co0.504Fe1.496]B (Co0.179Fe0.821)A [Co0.621Fe1.379]B (Co0.179Fe0.821)A [Co0.721Fe1.279]B (Co0.186Fe0.814)A [Co0.814Fe1.186]B (Co0.220Fe0.780)A [Co0.88Fe1.12]B (Co0.221Fe0.779)A [Co0.979Fe1.021]B
X-ray intensity ratio 7 0.005
CoxFe3 xO4 (0.5rx r1.2) nanoferrites have been prepared by auto-combustion citrate-precursor method with crystallite size ranging from 35–60 nm. XRD and IR data have confirmed the formation of single-phase samples for xZ0.7 while traces of hematite are present for x ¼0.5 and 0.6. TEM micrograph confirmed the nanoscale nature of the prepared powders. Both the lattice parameter and the crystallite size were correlated to the cation distribution in the B site and the presence of either hematite or other coexisting spinel phases, as observed from IR data. Magnetic parameters, IR spectra, XRD patterns, and lattice parameter were all used to propose a cation distribution that explain the complex relation between the recorded magnetization and coercivity and all of the crystallite size, sublattice radii, content of Co3 þ and Fe2 þ in B-site, and the existence of local canting effect. Reasonable matching between estimated cation distribution and experimental data was achieved.
576
572
251
1.2
388 386 384 382 0.679 380 0.674
378 0.6
0.8
1.0
1.2
Cobalt content (x) Fig. 10. Comparison of the variation of the sublattice radii, rA and rB, and the absorption peaks of the IR spectra, ν1 and ν2, with the cobalt content for CoxFe3-xO4 (0.5 rx r 1.2).
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